Geodesic
The prenucleolus of games with restricted cooperation
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 3 (2011) no. 4, pp. 23-48

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A cooperative game with restricted cooperation is a triple $(N,v,\Omega)$, where $N$ is a finite set of players, $\Omega\subset2^N$, $N\in\Omega$ is a collection of feasible coalitions, $v\colon\Omega\to\mathbb R$ is a characteristic function. The definition implies that if $\Omega=2^N$, then the game $(N,v,\Omega)=(N,v)$ is a classical cooperative game with transferable utilities (TU). The class of all games with restricted cooperation $\mathcal G^r$ with an arbitrary universal set of players is considered. The prenucleolus for the class is defined in the same way as for classical TU games. Necessary and sufficient conditions on a collection $\Omega$ providing existence and singlevaluedness of the prenucleoli for the class $\mathcal G^r$ are found Axiomatic characterizations of the prenucleolus for games with two-type collections $\Omega$ generated by coalitional structures are given.
Keywords: cooperative game, restricted cooperation, prenucleolus
Mots-clés : coalitional structure. 
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     author = {Ilya V. Katsev and Elena B. Yanovskaya},
     title = {The prenucleolus of games with restricted cooperation},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {23--48},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2011_3_4_a1/}
}
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Ilya V. Katsev; Elena B. Yanovskaya. The prenucleolus of games with restricted cooperation. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 3 (2011) no. 4, pp. 23-48. http://geodesic.mathdoc.fr/item/MGTA_2011_3_4_a1/